adding the trace of the trivial Hecke operator when computing primes

assaferan · Jun 23, 2023 · 8686eab · 8686eab
1 parent 6e284ae
commit 8686eab
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Showing 3 changed files with 16 additions and 9 deletions.
diff --git a/Tests/MagmaFormula.m b/Tests/MagmaFormula.m
@@ -17,7 +17,7 @@ procedure testPariVSMagma(N,k : New := false, OnlyPrimes := false, Prec := 1000)
     r := r[start..fin];
     traces_AL := [StringToInteger(x) : x in Split(r, ",")];
     trace_func := New select TraceFormulaGamma0ALNew else TraceFormulaGamma0AL;
-    val_list := OnlyPrimes select PrimesUpTo(Prec) else [0..Prec];
+    val_list := OnlyPrimes select [1] cat PrimesUpTo(Prec) else [0..Prec];
     traces_magma := [trace_func(n, N, k) : n in val_list];
     assert traces_magma eq traces_AL[1..#val_list];
     return;

diff --git a/Tests/ModSym.m b/Tests/ModSym.m
@@ -6,7 +6,7 @@
 procedure testPariVSMS(N,k,n : New := false)
     is_prime := IsPrime(n);
     if (is_prime) then
-	n_idx := #PrimesUpTo(n);
+	n_idx := #PrimesUpTo(n) + 1;
     else
 	if (New) then
 	    printf("Error! Only supports newsubspace for prime Hecke operators!\n");
@@ -25,9 +25,6 @@ procedure testPariVSMS(N,k,n : New := false)
     fin := Index(r, "]") - 1;
     r := r[start..fin];
     traces_AL := [StringToInteger(x) : x in Split(r, ",")];
-    // C := CuspidalSubspace(ModularSymbols(N,k,1));
-    // al := AtkinLehner(C,N);
-    // T := HeckeOperator(C,n);
     assert traces_AL[n_idx] eq get_trace(N,k,n : New := New); // Trace(al*T);
     return;
 end procedure;

diff --git a/src/traceAL_tools.c b/src/traceAL_tools.c
@@ -637,19 +637,24 @@ GEN traceALprimes(long N, long k, long prec, int newspace)
 {
   GEN p_list = primes0(mkvec2(mkintn(1,1), nextprime(mkintn(1,prec))));
   long num_primes = lg(p_list);
-  GEN res = cgetg(num_primes-1, t_VEC);
+  // adding also the trace for T_1 = 1
+  // GEN res = cgetg(num_primes-1, t_VEC);
+  GEN res = cgetg(num_primes, t_VEC);
   long p;
 
   GEN (*trace_func)(long, long, long);
   trace_func = (newspace ? &traceALNew : &traceAL);
 
   // printf("In traceALprimes. num_primes = %ld. newspace = %d. \n", num_primes, newspace);
   // printf("trace_func = %x.\n", (unsigned int)trace_func);
+
+  gel(res, 1) = (newspace ? traceALNewTrivial(N,k) : traceAL(N,1,k));
 
   for (long idx = 1; idx < num_primes - 1; idx++)
   {
     p = gtos(gel(p_list, idx));
-    gel(res, idx) = (*trace_func)(N, p, k);
+    // gel(res, idx) = (*trace_func)(N, p, k);
+    gel(res, idx+1) = (*trace_func)(N, p, k);
   }
   return res;
 }
@@ -658,15 +663,20 @@ GEN trace_primes(long N, long k, long prec, int newspace)
 {
   GEN p_list = primes0(mkvec2(mkintn(1,1), nextprime(mkintn(1,prec))));
   long num_primes = lg(p_list);
-  GEN res = cgetg(num_primes-1, t_VEC);
+  // adding trace of the identity (dimension of the space)
+  // GEN res = cgetg(num_primes-1, t_VEC);
+  GEN res = cgetg(num_primes, t_VEC);
   long p;
   GEN NK = mkvec2(mkintn(1,N),mkintn(1,k));
   GEN f = mftraceform(NK,newspace ? 0 : 1);
+
+  gel(res, 1) = mfcoef(f, 1);
 
   for (long idx = 1; idx < num_primes - 1; idx++)
   {
     p = gtos(gel(p_list, idx));
-    gel(res, idx) = mfcoef(f, p);
+    // gel(res, idx) = mfcoef(f, p);
+    gel(res, idx+1) = mfcoef(f, p);
   }
   return res;
 }